The Issue with Floating Point
In a python REPL environment, we would see the following:
1 2 3 

That is x
is not actually stored as 0.1
. This is because \(\dfrac{1}{10}\) cannot be represented as a finite combination of these:
\[ \dfrac{a_1}{2} + \dfrac{a_2}{2^2} + \dfrac{a_3}{2^3} + \cdots . \]
In other words, there is no corresponding binary fraction for 0.1
.
Which of the following can be expressed without any error as a floating point?